Defects on Шоттки and Френкелю

Defects on Шоттки and Френкелю


The defects on Шоттки and Френкелю concern to the thermal equilibrium defects connected to a disorder arrangement in a lattice of a crystal of "own" particles (of atoms or ions). Such arrangement arises, if the particle leaves(abandons) the regular rule(situation) in unit of a lattice, leaving his(its) free (vacant). There are two opportunities of education of defects in a lattice at the expense of moving particles from its(her) units. One of them was постулирована I. And. Френкелем, another - In. Шоттки.

The atom or ion can move from unit of a lattice, leaving there vacancy, in междоузлие, removed from unit on some distance.

Such defect as pair vacancy - междоузельный atom (ion) is called as defect on Френкелю (fig. 11, а). If atom (ion) leaves(abandons) unit of a lattice, leaving in him vacancy, and leaves for limits of a lattice on a surface of a crystal, completing her(it), in a lattice there are only vacancies. Such type of defect as free (vacant) units of a lattice is called as defect on Шоттки (fig. 11,6).



The basic reason of education of defects on Френкелю and Шоттки are the thermal fluctuations of atoms (ions). The average amplitude of fluctuation of atoms at usual temperatures is rather small (? 5... 10 % from size of the period of a lattice).

Fig. 11. The schematic image of defects on Френкелю (а) and on Шоттки (б) (in - ideal lattice)

However atoms in a lattice make thermal fluctuations not strictly in coordination, therefore even in these conditions at the expense of power флуктуации one of atoms can receive from next energy, sufficient for his(its) output(exit) from unit of a lattice. Especially this process occurs at the raised(increased) temperatures, at which the amplitude of fluctuation of atoms strongly grows. Thus, any crystal which is taking place at temperature, distinct from absolute zero, will contain always certain number of the specified thermal defects.

For education of defects on Френкелю and Шоттки the certain expenses of energy (energy of activation of process of education of defect) are required, however it is accompanied by increase энтропии at the expense of increase of a degree разупорядоченности of a lattice, that causes reduction of energy Гиббса. Hence, the education of similar defects appears energetically favourable and results in increase of stability of a crystal. From here follows, that the thermal defects on Френкелю and Шоттки are equilibrium and to each temperature there corresponds(meets) their certain equilibrium concentration in a crystal.

From the given equations follows, that the equilibrium concentration of defects on Шоттки and Френкелю is экспоненциальной function of temperature and energy of activation. Increase of temperature and accordingly reduction of energy of activation result in increase of equilibrium concentration of defects.

The energy of activation of process of education of dot defects depends on their type, chemical nature of substance and his(its) structure, therefore, though at a lattice of any not molecular crystal there are simultaneously all kinds of dot defects, one of them (with smaller energy of activation) usually prevail above others. The energy of education of defects on Шоттки with other things being equal is less, than defects on Френкелю, as accommodation of atom in междоузлии requires(demands) usually significant power expenses

For example, the defects on Френкелю will arise more easy in crystals with structure having large emptiness, or then, when the sizes аниона and катиона strongly differ, as all this facilitates accommodation катионов in междоузлиях.

Defects on Френкелю in the pure state, т. е. When the number of vacancies is equal to number межузельных of atoms, can take place only in crystals стехиометрического of structure, in real crystals with coordination lattices it, as a rule, is not observed. The defects on Шоттки can arise at the expense of education both катионных, and анионных of vacancies. In ионных crystals often there is energetically to more favourable an education of pairs vacancies, т. е. The education of vacant unit on a place катиона and аниона, as thus is more easy saved an electroneutrality of a surface of a crystal and lattice as a whole. However basically it is not necessary and in real crystals equality thermal катионных and анионных of vacancies can and not be observed.


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The dot nuclear defects in a crystal lattice have the certain properties. For example, the vacancies in ионных crystals act by carriers of a charge, and катионная the vacancy bears(carries) negative, and анионная - a positive charge. Certainly, actually charge in vacancy does not contain, but electrical field, arising around of it,(her,) same, what would arise, if in vacancy the charge, on meaning(importance) equal settled down, and on a mark opposite to a charge of an ion, which has left(abandoned) given unit of a lattice. Any dot defects have ability to migration (диффузии) in a crystal lattice as a result of thermal флуктуации or application to a crystal of an external electrical field. For example, катион in междоузлии can pass at the appropriate excitation in next междоузлие, vacancy мигрируют at the expense of moving the next ion to vacant unit, т. е. By a consecutive exchange of positions between ions and vacancies (at such so-called вакансионном the mechanism диффузии the moving of vacancies in one direction is equivalent to moving of ions in the friend). The dot defects can cooperate with each other, forming in the elementary case ассоциаты - defects borrowing(occupying) next кристаллографические of a position. For example, in a lattice there can be connected groups of vacancies (кластеры). The connected pairs vacancies are capable диффундировать faster, than the isolated vacancies, and threefold кластеры are even faster.

The presence in crystals of dot defects on Шоттки and Френкелю renders essential influence on many properties of crystal ph. In particular, their presence at a crystal and ability to migration cause ионную electrical conductivity and processes массопереноса (диффузии) in a crystal lattice (in бездефектном an ideal crystal the process массопереноса practically is impossible). In this connection the presence of dot defects strongly accelerates such important in technology силикатов and refractory not metal materials processes, as твердофазовые of reaction, sintering, рекристаллизацию and т. д., which speed is defined(determined) by speed диффузии of material particles. The education of defects on Шоттки results in increase of volume of a crystal (crystal as though "swells" for the bill достраивания from a surface by atoms excluded from units of a lattice) and downturn of his(its) density (education of defects on Френкелю anyway as a first approximation does not result in change of density).




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